Theorems · Theorem · algebraic topology

Topology.RelCWComplex.isClosed_inter_cellFrontier_succ_of_le_isClosed_inter_closedCell

∀ {X : Type u_1} [t : TopologicalSpace X] {C D : Set X} [inst : Topology.RelCWComplex C D] [T2Space X] {A : Set X}
  {n : ℕ},
  (∀ m ≤ n, ∀ (j : Topology.RelCWComplex.cell C m), IsClosed (A ∩ Topology.RelCWComplex.closedCell m j)) →
    ∀ (j : Topology.RelCWComplex.cell C (n + 1)),
      IsClosed (A ∩ D) → IsClosed (A ∩ Topology.RelCWComplex.cellFrontier (n + 1) j)

If for all m ≤ n and every i : cell C m the intersection A ∩ closedCell m j is closed and A ∩ D is closed then A ∩ cellFrontier (n + 1) j is closed for every j : cell C (n + 1).

Defined in

Mathlib.Topology.CWComplex.Classical.Basic

Cited by

2 results in Mathlib

Foundations

Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopology.RelCWComplexT2Space